Changing colors for BGE
There's two ways to change object colors in real time: through Object Color material's option, or through material node's Hue/Saturation (available in realtime only in UPBGE).

Object Color

This one is pretty simple:


Enable the Object Color checkbox on the desired material.
Change the Object Color in realtime by animating it.




Example file: 

Hue/Saturation Node

This one is a bit more complex, but a lot more powerful and with better results. Remember this one ONLY is possible in realtime on UPBGE.


Go to Node Editor and enable the node compositing for the desired material.
Add an Hue/Saturation node between the Material node and the Output node.
Separate the RGB colors of the object and set the hue value to the red value.
Animate the red color on Object Color to change the hue in realtime.




Example file: